Group theory in design of experiments

Hello,
I have been following the works of Diaconis, Viana and van de Ven and have a query about the approach taken in van de Ven's dissertation ("Equivalences in Design of Experiments").
My understanding is that van de Ven's approach does not take replication into account and that he therefore does not need to consider wreath products (which Diaconis invokes when there are replications).
Is that right?